Modelos discretos para agregação populacional

• Ano de defesa: 2019
• Autor(a) principal: Rossato, Marcelo Cargnelutti
• Tipo de documento: Dissertação
• Tipo de acesso: Acesso aberto
• Idioma: por
• Instituição de defesa: Universidade Federal de Santa Maria; Brasil; Matemática; UFSM; Programa de Pós-Graduação em Matemática; Centro de Ciências Naturais e Exatas
• Palavras-chave em Português: Agregação; Formação de padrões espaciais; Movimentação dependente da densidade; Redes de mapas acoplados; Aggregation; Spatial pattern formation; Density-dependent movement; Coupled map networks; CNPQ::CIENCIAS EXATAS E DA TERRA::MATEMATICA
• Link de acesso: http://repositorio.ufsm.br/handle/1/19763

The mechanisms that can lead to the formation of heterogeneous distribution of individuals of many biological species arouse the interest of researchers from various areas. Many mathematical models of pattern formation are based on the Turing mechanism and on aggregation processes in relation to concentration gradients of a chemical substance. Recently, the Cahn-Hilliard principle of phase separation, which assumes density-dependent movement, has been used to study self-organized mussel patterns. In this work, we formulate three discrete models of coupled map networks with density-dependent movement to describe processes of aggregation and formation of spatial patterns. Some species show better development at intermediate densities, avoiding problems related to overpopulation or the difficulty of keeping the species at low population densities. Thus, the first model considers only the local perception of individuals for movement, while in the other two it is taken into account that they have a sharper sensory capacity and also analyze conditions at nearby sites. Several discrete model simulations were performed for several parameter sets and the continuous formulations corresponding to each one of the models were obtained. The resulting spatial patterns were classified as homogeneous, stable heterogeneous, oscillatory heterogeneous or unstable. Thus, we conclude that the three proposed models can represent aggregation mechanisms and that this process occurred more effectively considering that individuals can perceive not only the density at their site, but also at neighboring sites.